3.681 \(\int \frac{\left (-3+2 \sqrt{x}\right ) \left (-3 \sqrt{x}+x\right )^{2/3}}{\sqrt{x}} \, dx\)

Optimal. Leaf size=17 \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]

[Out]

(6*(-3*Sqrt[x] + x)^(5/3))/5

_______________________________________________________________________________________

Rubi [A]  time = 0.0845331, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Int[((-3 + 2*Sqrt[x])*(-3*Sqrt[x] + x)^(2/3))/Sqrt[x],x]

[Out]

(6*(-3*Sqrt[x] + x)^(5/3))/5

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 6.32127, size = 14, normalized size = 0.82 \[ \frac{6 \left (- 3 \sqrt{x} + x\right )^{\frac{5}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x-3*x**(1/2))**(2/3)*(-3+2*x**(1/2))/x**(1/2),x)

[Out]

6*(-3*sqrt(x) + x)**(5/3)/5

_______________________________________________________________________________________

Mathematica [A]  time = 0.0212846, size = 17, normalized size = 1. \[ \frac{6}{5} \left (x-3 \sqrt{x}\right )^{5/3} \]

Antiderivative was successfully verified.

[In]  Integrate[((-3 + 2*Sqrt[x])*(-3*Sqrt[x] + x)^(2/3))/Sqrt[x],x]

[Out]

(6*(-3*Sqrt[x] + x)^(5/3))/5

_______________________________________________________________________________________

Maple [A]  time = 0.013, size = 12, normalized size = 0.7 \[{\frac{6}{5} \left ( x-3\,\sqrt{x} \right ) ^{{\frac{5}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x-3*x^(1/2))^(2/3)*(-3+2*x^(1/2))/x^(1/2),x)

[Out]

6/5*(x-3*x^(1/2))^(5/3)

_______________________________________________________________________________________

Maxima [A]  time = 0.946612, size = 24, normalized size = 1.41 \[ \frac{6}{5} \,{\left (x^{\frac{4}{3}} - 3 \, x^{\frac{5}{6}}\right )}{\left (\sqrt{x} - 3\right )}^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="maxima")

[Out]

6/5*(x^(4/3) - 3*x^(5/6))*(sqrt(x) - 3)^(2/3)

_______________________________________________________________________________________

Fricas [A]  time = 0.305304, size = 15, normalized size = 0.88 \[ \frac{6}{5} \,{\left (x - 3 \, \sqrt{x}\right )}^{\frac{5}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="fricas")

[Out]

6/5*(x - 3*sqrt(x))^(5/3)

_______________________________________________________________________________________

Sympy [A]  time = 3.90253, size = 36, normalized size = 2.12 \[ - \frac{18 \sqrt{x} \left (- 3 \sqrt{x} + x\right )^{\frac{2}{3}}}{5} + \frac{6 x \left (- 3 \sqrt{x} + x\right )^{\frac{2}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x-3*x**(1/2))**(2/3)*(-3+2*x**(1/2))/x**(1/2),x)

[Out]

-18*sqrt(x)*(-3*sqrt(x) + x)**(2/3)/5 + 6*x*(-3*sqrt(x) + x)**(2/3)/5

_______________________________________________________________________________________

GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (x - 3 \, \sqrt{x}\right )}^{\frac{2}{3}}{\left (2 \, \sqrt{x} - 3\right )}}{\sqrt{x}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x),x, algorithm="giac")

[Out]

integrate((x - 3*sqrt(x))^(2/3)*(2*sqrt(x) - 3)/sqrt(x), x)